amistre64
  • amistre64
What are all the cosets of \(Z_4\) of \(Z_2\)?
Mathematics
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SOLVED
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schrodinger
  • schrodinger
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amistre64
  • amistre64
or would that be better notated as 4Z of 2Z ?
anonymous
  • anonymous
i think the first one
amistre64
  • amistre64
cosets of 4Z of Z 4Z = {...,-8,-4,0,4,8,...} 1+4Z = {...,-7,-3,1,5,9,...} 2+4Z = {...,-6,-2,2,6,10,...} 3+4Z = {...,-5,-1,3,7,11,...}

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anonymous
  • anonymous
\(\mathbb{Z}_4=\{0,1,2,3\}\) which has only one non - trivial subgroup \(\{0,2\}\)
anonymous
  • anonymous
so i am thinking you want the cosets of \(\{0,2\}\) maybe
amistre64
  • amistre64
i have the hardest time trying to decipher what the end of chapter problems are actually asking for :)
amistre64
  • amistre64
i noticed something a few minutes ago with respect to permutations and mod n
anonymous
  • anonymous
if it says exactly what you wrote, i am pretty sure it means what i wrote since \(\{0,2\}\) with addition mod 4 is the same as \(\{0,1\}\) with addition mod 2, i bet it is asking for the cosets of that
amistre64
  • amistre64
ill delve further into it tonight ... to see if ive got some misinformation seeping about me noggin
anonymous
  • anonymous
k have fun
amistre64
  • amistre64
http://faculty.clayton.edu/Portals/455/Content/MATH3110-SP13/HW/M3110SP13-HW09-SOL.pdf this seems to be it ....
amistre64
  • amistre64
i sense the {0,2} in that
anonymous
  • anonymous
lol well then i was wrong , wasn't i? it was the second thing you wrote
amistre64
  • amistre64
i spose i could interpret: find all cosets of nZ of kZ list nZ, then add on the elements of kZ keep the uniques sets
anonymous
  • anonymous
yeah pretty clear that in your case there will be only two right? the set of integers divisible by 4, and the set of integers divisible by 2 but not by 4
amistre64
  • amistre64
yep

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